Bio Statistics
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homework.docxGastroenterology
Two drugs (A, B) are compared for the medical treatment of duodenal ulcer. For this purpose, patients are carefully matched with regard to age, gender, and clinical condition. The treatment results based on 200 matched pairs show that for 89 matched pairs both treatments are effective; for 90 matched pairs both treatments are ineffective; for 5 matched pairs drug A is effective, whereas drug B is ineffective; and for 16 matched pairs drug B is effective, whereas drug A is ineffective.
1 What test procedure can be used to assess the results?
2 Perform the test in Problem 1, and report a p-value. In the same study, if the focus is on the 100 matched pairs con- sisting of male patients, then the following results are obtained: for 52 matched pairs both drugs are effective; for 35 matched pairs both drugs are ineffective; for 4 matched pairs drug A is effective, whereas drug B is ineffective; and for 9 matched pairs drug B is effective, whereas drug A is ineffective.
3 How many concordant pairs are there among the male matched pairs?
4 How many discordant pairs are there among the male matched pairs?
Cancer
A topic of current interest is whether abortion is a risk factor for breast cancer. One issue is whether women who have had abortions are comparable to women who have not had abortions in terms of other breast-cancer risk factors. One of the best-known breast-cancer risk factors is parity (i.e., number of children), with parous women with many children having about a 30% lower risk of breast cancer than nullipa- rous women (i.e., women with no children). Hence, it is im- portant to assess whether the parity distributions of women with and without previous abortions are comparable. The data in Table 1 were obtained from the Nurses’ Health Study on this issue.
TABLE 1 Parity distribution of women with abortions and women without abortions
|
Parity |
Induced abortion |
|
|
|
Yes |
No |
|
|
(n = 16,353) |
(n = 77,220) |
|
0 |
34% |
29% |
|
1 |
23% |
18% |
|
2 |
30% |
34% |
|
3 |
10% |
15% |
|
4+ |
3% |
4% |
6 What test can be performed to compare the parity distribution of women with and without induced abortions?
10.66 Implement the test in Problem 6, and report a two-tailed p-value. Suppose that with each additional child, breast-cancer risk is reduced by 10% (i.e., women with 1 child have a risk of breast cancer that is 90% of that of a nulliparous woman of the same age; women with 2 children have a risk that is .92 or 81% of that of a nulliparous woman, etc.). (For the purposes of this problem, consider women with 4+ births as having exactly 4 births.)
7 Suppose there is no causal effect of induced abor- tion on breast cancer. Based on the parity distribution in the two groups, would women with induced abortion be expected to have the same, higher, or lower risk of breast cancer? If higher or lower, by how much? (Assume that the age distributions are the same between women who have or have not had previous abortions.)
Health Promotion
It is fairly well known that perception of weight by adoles- cents does not always agree with actual weight. What is less clear is whether perception of weight differs by gender. For this purpose, a study was performed among students in a local high school, where students provided their actual height and weight by self-report. The following data were obtained from 280 students (140 boys and 140 girls). (The data for this problem were provided by Laura Rosner.) The students were classified as underweight if their body- mass index (BMI) (kg/m2) was less than 18.0 kg/m2, as normal if their BMI was ≥ 18.0 and < 25.0, and overweight if their BMI was ≥ 25.0. Based on these criteria, 16 of the girls were underweight, 112 were of normal weight, and 12 were overweight. For the boys, 6 were underweight, 114 were of normal weight, and 20 were overweight.
8 What test procedure can be used to assess whether the weight status of boys significantly differs from girls?
9 Perform the test procedure in Problem 8, and provide a two-tailed p-value.
